Missing Area Reconstruction in Multispectral Images Under a Compressive Sensing Perspective 

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Proposed Inpainting Strategies

The proposed strategies move in three different directions. The first one consists to enrich the feature space so that to refine the search for the most similar patch in the source region. This will be done by adding textural features extracted from the original image. Through isometric transformations, the second direction aims at increasing the amount of patch candidates and thus populating further the search space. The last direction faces the inpainting problem within a multiresolution processing scheme.

Feature extraction-based inpainting (FEBI)

As mentioned before, the first strategy intends to facilitate the search for the most similar patch by considering not just original image channels but also image features, which capture local image properties potentially useful for the best patch identification. Operationally speaking, this means applying RBI with a similarity function ( ) that integrates the extracted image features.
In this work, two kinds of image features are considered. The first expresses the local variance of the image (Stdv), while the second kind is a space-frequency representation of the original image by means of the symlet transform (Sym), which is a particular case of the wavelet transform [12]. In both cases, the similarity function (3.5) to minimize can be rewritten as:
where corresponds to the extracted feature (i.e., Stdv or Sym) andi is a weighting parameter which controls the influence of the extracted features on the search process.

Inpainting with isometric transformation (IsoI)

One of the potential problems of RBI is that the patch search is directionally constrained by the spatial image structure. By contrast, patches could be searched for in various directions for a better mining of the inpainting possibilities conveyed in the image. A second strategy we explore consists therefore to implement a patch search process by isometric geometrical transformations [13]. This means that the source patch will be transformed (rotated and/or flipped) to match better the target patch . In this work, a subset of seven common transformations is selected (see Figure 3.3).

Multiresolution inpainting (MRI)

The third and last strategy is based on a completely different idea motivated by the success it obtained in different image processing and analysis application fields [14]-[15]. It consists in a multiresolution processing of the image so that to reconstruct missing data with a progressively increasing spatial accuracy. In more detail, the algorithm starts by applying RBI with a patch of large window dimension to fill in the considered image hole (Figure 3.4). In the next iteration, the size of the patch is decreased and RBI is applied again with a first difference that this time missing data have been substituted by an estimate obtained in the previous iteration. In order to maintain a memory between successive resolution levels, another difference is that instead of performing a simple pasting of the new patch, the reconstruction will be based on a weighted sum of the new patch and the one found at previous resolution. This process is repeated up to reach the
predefined smallest value of .

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Table of contents :

1. Introduction and Thesis Overview
1.1. Context
1.2. Problems
1.3. Thesis Objective, Solutions and Organization
1.4. References
2. Résumé Long en Français
2.1. Contexte
2.2. Problèmes
2.3. Objectif thèse, Solutions et Organisation
2.4. Références
3. Inpainting Strategies for Reconstruction of Missing Data in VHR Images
3.1. Introduction
3.2. Problem Formulation
3.2.1. Region-based inpainting (RBI)
3.3. Proposed Inpainting Strategies
3.3.1. Feature extraction-based inpainting (FEBI)
3.3.2. Inpainting with isometric transformation (IsoI)
3.3.3. Multiresolution inpainting (MRI)
3.4. Experimental Results
3.4.1. Dataset description and setups
3.4.2. Experimental results
3.5. Conclusion
3.6. Acknowledgment
3.7. References
4. Support Vector Regression with Kernel Combination for Missing Data Reconstruction 
4.1. Introduction
4.2. Problem Formulation
4.3. Proposed Solution
4.3.1. ε-insensitive support vector regression
4.3.2. Common kernel functions
4.3.3. Kernel function
4.3.4. Feature Vector
4.4. Experimental Results
4.4.1. Dataset description
4.4.2. Experiments
4.4.3. Comparative analysis
4.5. Conclusion
4.6. Acknowledgment
4.7. References
5. Missing Area Reconstruction in Multispectral Images Under a Compressive Sensing Perspective 
5.1. Introduction
5.2. Problem Formulation
5.3. Reconstruction via Compressive Sensing
5.3.1. Generalities on Compressive Sensing
5.4. Genetic Algorithm
5.4.1. General Concepts on GA
5.4.2. GA setup
5.5. Experimental Results
5.5.1. Dataset description and setup
5.5.2. Results
5.5.3. Reconstruction impact on image classification
5.6. Conclusion
5.7. Acknowledgement
5.8. References
6. A Complete Processing Chain for Shadow Detection and Reconstruction in VHR Images 
6.1. Introduction
6.2. Problem Formulation
6.3. Proposed Method
6.3.1. Mask construction
6.3.2. Border creation
6.3.3. Classification maps
6.3.4. Shadow reconstruction
6.3.5. Border reconstruction
6.4. Experimental Results
6.4.1. Border reconstruction
6.4.2. Experimental setup and results
6.4.3. Reconstruction impact on classification accuracy
6.4.4. Comparative analysis
6.5. Conclusion
6.6. Acknowledgment
6.7. References
7. Assessing the Reconstructability of Shadow Areas in VHR Images
7.1. Introduction
7.2. Shadow Reconstruction Methods
7.2.1. Linear transformation (LT)
7.2.2. Histogram matching (HM)
7.2.3. Gamma correction (GC)
7.3. Reconstructability Problem Formulation
7.4. Proposed Criteria
7.4.1. Histogram quantization error (HQE)
7.4.2. Gray level ratio (GLR)
7.4.3. Two sample Kolmogorov-Smirnov test (2KS)
7.4.4. Variance Ratio (VR)
7.4.5. Negentropy difference (ND)
7.4.6. Kullback-Leibler Divergence (DKL)
7.4.7. Angular Second-Moment Difference (ASMD)
7.4.8. Homogeneity Difference (HD)
7.5. Criterion Selection and Decision Making
7.5.1. Criterion selection
7.5.2. Reconstruction evaluation
7.6. Experimental Results
7.6.1. Dataset description
7.6.2. Experimental setup
7.6.3. Results
7.6.4. Validation of the Results
7.7. Conclusion
7.8. Acknowledgment
7.9. References
8. Conclusion
9. List of Related Publications
9.1. Published Journal Papers
9.2. Journal Papers in Revision
9.3. Conference Proceedings

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